Adaptive wavelet method for euler equation solution algorithm

Abstract

An adaptive wavelet method is proposed to reduce the computational workload, while preserving the numerical accuracy of original Euler equation solver. By the wavelet transformation, an adaptive sparse point dataset for the solution is constructed and fluxes are evaluated only at the cells within the adaptive dataset. On top of this basic adaptive wavelet framework, some additional numerical techniques are applied to preserve the numerical accuracy of conventional CFD solvers. First, the threshold value is modified to preserve the temporal accuracy as well as the spatial accuracy of conventional schemes by switching between the original threshold value and the magnitude of the spatial or temporal truncation error. Secondly, a stabilization technique is implemented to improve the compression ratio by controlling the numerical errors that comes from the insertion of the points into the computational domain. Thirdly, for the points that do not belong to the wavelet dataset, residual interpolation is employed rather than flux interpolation. Therefore, it is not necessary to add several additional cells to a dataset, otherwise which are definitely necessary in previous wavelet methods. Lastly, if the variations of flow variables are below the threshold value at the excluded points, then the tiny variations are checked and controlled during the time integration, which ensures the convergence acceleration in steady state flow problems. This new adaptive wavelet method is applied to steady and unsteady flow problems and substantial enhancement can be achieved in terms of the efficiency and the convergence without compromising the accuracy of the solution ? 2010 by World Scientific Publishing Co. Pte. Ltd. All rights reserved.